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Since R 20 of Eq. (3.8) is the resistance of the conductor at 20°C and
T 1 � 20°C is the change in temperature from 20°C, Equation (3.8) can
be written in the following form:
(3.9)
providing an equation for resistance in terms of all the controlling parameters.
PPM/°C
l
R � r��[1 � a20 DT ]
A
For resistors, as for conductors, resistance changes with a change in
temperature. The specification is normally provided in parts per million
per degree Celsius (PPM/°C), providing an immediate indication of the
sensitivity level of the resistor to temperature. For resistors, a 5000-PPM
level is considered high, whereas 20 PPM is quite low. A 1000-PPM/°C
characteristic reveals that a 1° change in temperature will result in a
change in resistance equal to 1000 PPM, or 1000/1,000,000 � 1/1000 of
its nameplate value—not a significant change for most applications.
However, a 10° change would result in a change equal to 1/100 (1%) of
its nameplate value, which is becoming significant. The concern, therefore,
lies not only with the PPM level but with the range of expected
temperature variation.
In equation form, the change in resistance is given by
DR � � Rnominal �(PPM)(DT 6
)
10
(3.10)
where R nominal is the nameplate value of the resistor at room temperature
and DT is the change in temperature from the reference level of
20°C.
EXAMPLE 3.12 For a 1-k� carbon composition resistor with a PPM
of 2500, determine the resistance at 60°C.
Solution:
1000 �
DR � �6 (2500)(60°C � 20°C)
10
� 100 �
and R � Rnominal � DR � 1000 ��100 �
� 1100 �
3.6 SUPERCONDUCTORS
There is no question that the field of electricity/electronics is one of the
most exciting of the 20th century. Even though new developments appear
almost weekly from extensive research and development activities, every
once in a while there is some very special step forward that has the whole
field at the edge of its seat waiting to see what might develop in the near
future. Such a level of excitement and interest surrounds the research
SUPERCONDUCTORS ⏐⏐⏐ 71